$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\Oof}[1]{\mathcal{O}(#1)} $$

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Error in amplification factors

Focus: the error measure \( A-\Aex \) as function of \( \Delta t \) (recall that \( p=a\Delta t \)): $$ \begin{equation} A-\Aex = \left\lbrace\begin{array}{ll} \Oof{\Delta t^2}, & \hbox{Forward and Backward Euler},\\ \Oof{\Delta t^3}, & \hbox{Crank-Nicolson} \end{array}\right. \end{equation} $$

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